https://file.aiquickdraw.com/mathbot/file/1729106565575xy0qtglo.jpg

Which equation best represents the relationship between x
 and y
?​​​​​​​
A.y=50x+100

B.y=100x+50

C.y=−50+100

D.y=100x−50



The graph shows a linear relationship between the number of months ($x$) and the money saved ($y$), and the slope is positive, indicating a direct increase in savings over time.

### Steps to determine the equation:

1. **Identify the slope (rate of saving per month):**
   - From the graph, after 1 month, the savings increase by $100.
   - This suggests that the slope $m$ (rate of savings per month) is 100.

2. **Find the y-intercept:**
   - The graph crosses the y-axis at $50, so the y-intercept $b = 50$.

3. **Form the equation of the line:**
   Using the slope-intercept form $y = mx + b$:
   - $m = 100$ (slope),
   - $b = 50$ (y-intercept).

Thus, the equation that represents the relationship between $x$ and $y$ is:
\[
y = 100x + 50
\]

### Correct Answer: 
**B. $y = 100x + 50$**

Would you like more details on how to calculate the slope or intercept?

Here are 5 related questions for further exploration:
1. How would the equation change if the y-intercept was $100 instead of $50?
2. What does the slope of 100 tell you in the context of this problem?
3. How do you find the equation of a line given two points on a graph?
4. If the slope was negative, how would that affect the interpretation of the graph?
5. Can you calculate the money saved after 6 months using the equation?

**Tip:** The slope in linear equations represents the rate of change, so in real-life contexts like this, it shows how fast one variable changes relative to another.

Which equation best represents the relationship between x and y?

Explore the relationship between time in months and money saved using the linear equation y = 100x + 50. Understand the concepts of slope and y-intercept as they relate to real-world financial planning. Suitable for students in Grades 6-8.

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